Duality Theory

Duality Theory in optimization is a mathematical concept that shows a deep connection between a primary problem (the "primal") and a related, secondary problem (the "dual"). Solving either problem provides insights into the other. Typically, the dual problem offers bounds or constraints that help determine the best solution for the primal problem. This relationship helps optimize complex systems efficiently, ensuring solutions meet all necessary conditions and constraints. In short, duality reveals how two interconnected problems influence each other, enabling better understanding and more effective solutions in fields like economics, engineering, and operations research.